Question: Solve for $x$ and $y$ using elimination. ${-x+4y = 33}$ ${x+5y = 57}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $9y = 90$ $\dfrac{9y}{{9}} = \dfrac{90}{{9}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-x+4y = 33}\thinspace$ to find $x$ ${-x + 4}{(10)}{= 33}$ $-x+40 = 33$ $-x+40{-40} = 33{-40}$ $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ You can also plug ${y = 10}$ into $\thinspace {x+5y = 57}\thinspace$ and get the same answer for $x$ : ${x + 5}{(10)}{= 57}$ ${x = 7}$